Very effective tool: Saturate your wicking compression undershirt in cool water before you put it on. It cools you for almost an hour, and doesn't really feel very wet. Even pouring a few capfuls of ice water down your chest and back during a game helps to refresh the effect.
Also, this is the age-old cooling remedy:
Shop online Aromatic Ammonia Spirit By Cumberland Swan - 2 Oz at AmericaRx.com
You just pour a bottle of this stuff in a tub of ice water and soak towels and handkerchiefs in it. Dab off with these towels and/or line your cap with a handkerchief. (When you see an MLB trainer come out with a wet towel to assist the umpire, quite often it's a towel dipped in an ammonia water solution.)